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Chelyshkov collocation approach for solving linear weakly singular Volterra integral equations

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Abstract

The purpose of this paper is to present a new numerical algorithm for solving the weakly singular Volterra integral equations. The operational matrix of fractional integral based on fractional-order Chelyshkov polynomials is constructed and together with the collocation method is used to reduce the integral equation into a system of algebraic equations. The convergence of the method is discussed in \(L^{2}\)-norm and finally, some numerical examples are shown to illustrate the accuracy of the proposed method.

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Authors and Affiliations

  1. Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran

    Y. Talaei

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  1. Y. Talaei
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Talaei, Y. Chelyshkov collocation approach for solving linear weakly singular Volterra integral equations. J. Appl. Math. Comput. 60, 201–222 (2019). https://doi.org/10.1007/s12190-018-1209-5

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  • DOI: https://doi.org/10.1007/s12190-018-1209-5

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